STMicroelectronics A 200 W ripple-free input current PFC pre-regulator with the L6563S EVL6563S-200ZRC EVL6563S-200ZRC Data Sheet
Product codes
EVL6563S-200ZRC
Zero-ripple current phenomenon: theory
AN3180
8/39
Doc ID 17273 Rev 1
Equation 6
and
are noteworthy because of their concision in expressing the conditions for
zero-ripple current phenomenon to occur, but unfortunately its physical nature is not shown.
To provide some physical insight, let us consider the a = n coupled inductor model (n is the
physical turn ratio N
To provide some physical insight, let us consider the a = n coupled inductor model (n is the
physical turn ratio N
2
/N
1
) excited by equal terminal voltages v(t), shown in
Figure 6.
Coupled inductor a = n model under zero-ripple current conditions
Proceeding with the same technique, in order for the ripple current i
2
(t) to be zero, the
voltage across the secondary leakage Ll
2
must be zero, that is, the voltages on either side of
Ll
2
must be equal to one another. On the other hand, if i2(t)=0 the voltage impressed on the
primary side of the ideal transformer v'(t) is given by the ratio of the inductive divider made
up of the primary leakage inductance Ll
up of the primary leakage inductance Ll
1
and the magnetizing inductance L
M
; the voltage
applied to the left-hand side of Ll
2
is equal to nv'(t). Then, there is zero-ripple current on the
secondary side of the coupled inductor if the following condition is fulfilled:
Equation 7
which is equivalent to
, as can be easily shown, considering that L
M
= M/n.
provides the desired physical interpretation of the zero-ripple current condition: it
occurs when the turn ratio exactly compensates for the primary winding leakage flux, so that
the primary winding induces, by transformer effect, a voltage identical to its own excitation
voltage on the secondary winding; and so, if this is externally excited by the same voltage,
no ripple current flows through it.
the primary winding induces, by transformer effect, a voltage identical to its own excitation
voltage on the secondary winding; and so, if this is externally excited by the same voltage,
no ripple current flows through it.
The extensions of this interpretation to the case of zero-ripple primary current (just reflect
the magnetizing inductance L
the magnetizing inductance L
M
to the secondary side) and to that of proportional excitation
voltages (
α ≠ 1) are obvious.
1
L
M
L
L
k
k
1
1
2
=
=
=
e
n
!-V
L
W
L
W
Q
Y W
Y W
/
0
/
O
/
O
L
0
W
LGHDO
Y W
Y
W
1
L
L
L
L
L
(t)
(t)
L
L
L
1
M
M
1
M
M
1
M
=
=
+
⇒
=
+
n
n
v
v
n
l
l